Cake: Preheat oven to 350°.,Using an electric mixer, cream the sugar and shortening until light and fluffy.,Sift or mix the flour, baking powder and salt.,While beating, add the dry mixture to the creamed mixture, alternating with the milk.,Then beat for 2- 2 1/2 minutes at medium speed.,Add the egg whites and almond extract.,Beat another 1 1/2 minutes.,Add the coconut and stir well.,Put into 2 greased and floured 9" cake pans.,Bake about 30 minutes or until a toothpick inserted in the center comes out clean.,Cool 10 minutes before removing layers from pans.,Spread apricot filling on completely cooled bottom layer.,Place second layer over filling.,Cover top and sides of both layers with frosting.,Filling: Drain apricots, reserving 2 Tbsp of juice.,Remove any pit fragments or pieces of stems from the apricots.,Puree in blender until smooth.,Place in saucepan.,Add reserved juice to cornstarch and mix well.,Stir into apricots.,Add the sugar.,Cook stirring over medium heat until thickened.,______,Add powdered sugar and vanilla extract.,If frosting is too stiff to spread, add milk a half teaspoon at a time.,After cake is frosted, lightly press more coconut onto the top and sides, if desired.